For a
better understanding of the Darwin correction one can look at
Ref. [1]}. In our case \({\bf v}_s=0\)  and consequently there
will be no relativistic modification of \(V(r)\) . More over we do
not consider any general relativistic effects due to \(V(r)\)  into
account. We briefly comment on the general relativistic generalization
of the central force problem in section . In the present
article the background space-time is assumed to be flat.
